Towards a logical reconstruction of information retrieval theory

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We here expand on a previous paper concerning the role of logic in information retrieval (IR) modelling. In that paper, among other things, we had pointed out how different ways of understanding the contribution of logic to IR have sprung from the (always unstated) adherence to either the total or the partial knowledge assumption. Here we make our analysis more precise by relating this dichotomy to the notion of vividness, as used in knowledge representation, and to another dichotomy which has had a profound influence in database theory, namely the distinction between the proof-theoretic and the model-theoretic views of a database, spelled out by Reiter in his "logical econstruction of database theory". We show that precisely the same distinction can be applied to logical models of IR developed so far. The strengths and weaknesses of the adoption of either approach in logical models of IR are discussed.